An NBA source told the Globe that the Celtics have signed swingman Terrence Williams to a 10-day contract — and there’s a chance that Williams, who is heading here from China, could be in uniform when the Celtics face the Nuggets Tuesday.

Williams wasn’t with the team during its practice Monday. He is awaiting a clearance letter from the team he was playing for in China before he flies here, the source said.

Rivers said he wasn’t sure if Williams, who has played for three NBA teams, would be with the Celtics for their shootaround Tuesday morning. He did say that Williams worked out with the Celtics during the summer and that he “did a pretty good job.”

“He’s been in the league; that’s what impressed me,” said Rivers, who downplayed his comments on Williams because the signing isn’t official.

While the Celtics clearly need guards after losing Rajon Rondo and Leandro Barbosa, Williams, an athletic 6-foot-6-inch wing player, gives them a much-needed body, which, considering the heavy minutes everyone is playing, is a vital addition in itself.

The 25-year-old was drafted 11th overall by the New Jersey Nets in 2009. In 129 NBA games with the Nets, Rockets, and Kings, the former University of Louisville standout averaged 7.6 points and 2.5 assists in 20.2 minutes.

After his rookie year with the Nets, Williams was traded to Houston after he repeatedly broke team rules. He played just 11 games for the Rockets, who waived him, and he then joined Sacramento via a 10-day contract.

Williams stayed with the Kings through the rest of the 2011-12 season, then signed with Detroit as a free agent in October 2012. The Pistons waived him that month.

Most recently, Williams has been playing for the Guangdong Southern Tigers of the Chinese Basketball Association, where in 29 games he averaged 17.9 points, 3.4 rebounds, and 4.1 assists in 27 minutes.

In mid-February, Williams left that team, which currently is in first place in the standings, because of an undisclosed death in the family.

Williams’s athleticism and physicality could help the Celtics both in their up-tempo offensive scheme and on defense.

The Celtics aren’t known to shy away from players with character issues, and the veteran leadership of Kevin Garnett, Paul Pierce, and Rivers is a big reason for that.

“He knows what’s ahead of him,” said veteran guard Jason Terry, a fellow Seattle native who said he already has messaged Williams. “He knows this is a no-nonsense type group.

“There just hasn’t been a Kevin Garnett, or Paul, myself — guys that he can look up to and respect and I think that’s going to help his situation. I don’t know any particulars or anything [about his past]. What I do know is the kid works hard, he’s a Seattle kid. And so he’s welcome.”

Terry said he’s known Williams since Williams was in high school.

“Playing with him in the summer, playing against him, just seeing him and seeing his work ethic, I know he’s a tremendous talent,” Terry said. “A freakish athlete, can handle the ball, and he’s a physical guard. I just can’t wait to see him get an opportunity.”

Rivers had said that the Celtics would be patient in searching for players, but the team needs more bodies — quickly.

“We could use a little depth pretty much at every position,” Pierce said. “Practice has been a little tough. We don’t have six guards to match up on the four big men. Kevin’s going to need a rest in practice, I’m going to need a rest in practice the rest of the way so we can make a second-half push.”

Because the Celtics don’t have many trade assets or much financial flexibility, it will be difficult for the team to attract a top-tier player. Adding players via 10-day contracts is the most efficient move the team can make in the interim.

Rivers didn’t deny that the Celtics need more players, but he said they wouldn’t rush the process.

“We do need another guard; there’s no doubt about that,” Rivers said. “I think we need two guards, actually. But I told Danny [Ainge], if we can’t get what we want, we just won’t have it. We really need one if just for practice if nothing else. Other than that, we’ll see.”

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